1. Field of the Invention
The present invention relates to a technique for transforming two different shape models into an approximate shape sharing the same phase information and having different geometric information.
2. Description of the Prior Art
Three-dimensional (3D) morphing of two different shapes is readily implemented by use of computer graphics (abbreviated to CG hereunder) when models of the two shapes have different geometric information such as vertex positions (coordinates) but share the same phase information such as connective relations of polygons and vertexes. Three-dimensional morphing is a method for generating CG images wherein one 3D shape model transforms smoothly into another. The technique is utilized effectively in creating special effects of images illustratively for use with game machines and in movies.
To prepare shape data for 3D morphing involves primarily one of two methods: building beforehand two shape models in such a way that the shapes will correspond to each other in terms of model information sharing the same number of vertexes and of surfaces (polygons); and projecting given models into intermediate shapes representing two shapes. The latter method involves, more specifically, transforming the two shape models into mesh shapes of M.times.N vertexes (intermediate shapes) sharing the corresponding mesh vertexes (m, n). Illustrated in FIGS. 1A, 1B, 1C, 2, 3A and 3B are a conventional method for automatically determining which mesh shape vertexes (i.e., lattice points) are to correspond to which positions in the original shapes.
With the above conventional method in use, the original shape model A represented by polygons in FIG. 1A and the original shape model B expressed by polygons in FIG. 1B are projected illustratively onto a cylindrical mesh of FIG. 1C. As shown in FIG. 2, when a shape is represented by cylindrical coordinates (r, .theta., z), the coordinates of the point of intersection between the straight line defined by the following expression: ##EQU1## and the shape surface are regarded as the cylindrical coordinates of the mesh vertex (m, n) for the image of the shape projected onto the cylindrical mesh. In the expression (1), H denotes the length of the shape in the z-axis direction. To obtain an r value from the straight line of the expression (1) and from the shape data requires verifying whether each of all shape elements (polygons, etc.) in the shape model intersects the straight line given by the expression (1) above. Transformation from cylindrical coordinates to orthogonal coordinates is accomplished by use of the expression: ##EQU2## A shape model A' (FIG. 3A) and a shape model B' (FIG. 3B) based on the mesh shapes with all their vertexes obtained as outlined above are similar to the original shape models A and B. As such, the shape models A' and B' are conducive to being processed for 3D morphing wherein the vertex-to-vertex correspondence is easy to achieve.
In the description of the related art above, .theta. and z settings are assigned equally to each of the vertexes (m, n). In practice, to prepare a mesh shape optimally reflecting the original shape requires several interactive sessions of vertex editing for adjusting the .theta. and z settings so that the mesh vertexes are positioned to the characteristic parts of the original shape. Every time such adjustment is performed, a check must be made to see whether the straight line of the expression (1) above intersects each of all polygons involved. The process is inefficient in that it necessitates enormous amounts of computations. The same applies even if the intermediate shape may be varied.